In general, that type of device requires the tubes that are used to be well calibrated, and above all well supported in the nose so that the connection can be made properly leaktight. That is why the use of such devices is restricted to tubes of relatively small diameter for which the ratio of thickness over diameter is fairly large. With larger diameters, endpieces are fitted to the ends of the tubes, where such endpieces are made separately, with manufacturing tolerances that are under better control. The cost of couplings of that kind is naturally more expensive, particularly because of the need for prior assembly of endpieces onto tubes. In addition, when making an installation in situ, for example an installation for distributing a compressed fluid, it is often necessary to adjust the length of the tubes in the installation. It is then necessary for a tube to be connectable in the state in which it is then to be found, with a minimum amount of work being done on its cut end. This work consists in forming a bead, or more generally peripheral projections, on the tube so as to provide means for preventing the tube from moving axially in the coupling. This work leads to the tube being deformed, which is harmful for the leaktightness of the coupling. Finally, it should also be observed that in all devices in the state of the art, the sealing ring that is put into place is often injured or taken away by the end of the tube for coupling while it is being inserted into the tubular nose.